Trouble with mechanical physics

[fixixisfunmf]

A 70 kg trampoline artist jumps vertically upward from the top of a platform with a speed of 4.5 m/s. (Ignore small changes in gravitational potential energy.

(a) How fast is he going as he lands on the trampoline, 3.0 m below?
m/s
(b) If the trampoline behaves like a spring with spring stiffness constant 5.2 multiplied by 104 N/m, how far does he depress it?
m

I think i have to use kinematics but I don't really know how to execute it

A 1400 kg sports car accelerates from rest to 80 km/h in 7.4 s. What is the average power delivered by the engine?
I put 112000 W but it is wrong and I don't know what to do to get it write

please help me with one or both of these that would be great

 

[fluidistic]

For part (a), think about the conservation of mechanical energy. ($$E=\frac{mv^2}{2}+mgh$$).

For part (b), use Hook's law. (Check out wikipedia or google it).

 

[thomate1]

For part (a), you can use the equation for conservation of energy:

Initial kinetic energy (at the top of the platform) = Final kinetic energy (at the trampoline) + Final potential energy (at the trampoline)

Initial kinetic energy = (1/2)mv^2 = (1/2)(70 kg)(4.5 m/s)^2 = 708.75 J

Final kinetic energy = (1/2)mv^2 = (1/2)(70 kg)v^2

Final potential energy = mgh = (70 kg)(9.8 m/s^2)(3.0 m) = 2058 J

Setting these two equal to each other and solving for v, we get v = 7.0 m/s.

For part (b), we can use the equation for Hooke's Law:

F = kx

Where F is the force exerted by the trampoline, k is the spring stiffness constant, and x is the distance the trampoline is depressed.

The force exerted by the trampoline is equal to the weight of the artist, which is mg = (70 kg)(9.8 m/s^2) = 686 N.

Solving for x, we get x = F/k = (686 N)/(5.2 x 10^4 N/m) = 0.0132 m = 1.32 cm.

For the second question, we can use the equation for average power:

P = (Work done)/(Time taken)

The work done by the engine is equal to the change in kinetic energy of the car, which is given by:

Work = (1/2)mv^2 = (1/2)(1400 kg)(22.2 m/s)^2 = 435240 J

The time taken is given as 7.4 s.

Therefore, the average power delivered by the engine is P = (435240 J)/(7.4 s) = 58800 W.